Oscillations a: Romeo and Juliet

In this and the following four videos, we present some concepts that can be used to design and recognize mathematical models that support oscillatory behavior. In this first video, we show that oscillations can be viewed as cyclic loops in a 2-dimensional plane. One way to arrange for a pair of variables R and J to perform oscillations is to let the time-derivative of each variable be proportional to the value of the other variable, with a negative sign in the coefficient of one of these differential equations.